Proof of the Gour-Wallach conjecture

TL;DR

This paper proves a conjecture by Gour and Wallach regarding the characterization of maximally entangled four-qubit states using the hyperdeterminant measure, advancing understanding of quantum entanglement.

Contribution

It provides a rigorous proof of the Gour-Wallach conjecture, identifying the structure of maximally entangled four-qubit states based on hyperdeterminant values.

Findings

Confirmed the specific form of maximally entangled four-qubit states

Validated the hyperdeterminant as a measure of genuine entanglement

Enhanced theoretical understanding of quantum entanglement measures

Abstract

The absolute value of the hyperdeterminant of four qubits is a useful measure of genuine entanglement. We prove a recent conjecture of Gour and Wallach describing the pure maximally entangled four-qubit states with respect to this measure.